If \(\mathbf {Y}=(Y_1,\ldots ,Y_T)^\top \)  is a time series
vector,
then the copula \(C\)  at (REF ) with \(m=T\)  captures
the serial dependence in the series and is called a “time series copula”.
While there has been less work on time series copulas than those used to capture
cross-sectional dependence, they are increasingly being used for both time series data
(where there is a single observation on the vector \(\mathbf {Y}\) ) and
longitudinal data (where there are multiple observations on the vector \(\mathbf {Y}\) ).
Early contributions
include [1]}, [2]}, [3]},
[4]}, [5]} and [6]} for Markov processes,
[7]} for the implicit copulas of Gaussian processes popular in machine learning,
and [8]} for
vine copulas that exploit the time ordering of the
elements of \(\mathbf {Y}\) .
